1. Operations Management Session 24: Inventory Systems

2. Session 24 Operations Management2 Previous Lectures  EOQ Model Known demand, multi-periods  Newsvendor Model Uncertain demand, but only 1 period The tension between setup cost and inventory holding cost is not relevant.  How do we handle uncertain demand and multiple periods?

3. Session 24 Operations Management3 Today’s Lecture  Inventory systems  Inventory turns/turnover  Briefing on the simulation game

4. Session 24 Operations Management4 Inventory Level in Real Life First lead time, LT 1 d1d1 Q Amount used during first lead time Safety stock, SS LT 2 Order 1 placed Order 2 placed Order 3 placed Shipment 1 received Shipment 2 received Time Inventory on Hand Reorder point Order quantity, Q

5. Session 24 Operations Management5 Inventory Systems  Continuous (perpetual) system:  Continuous (perpetual) system: System that keeps track of removals from inventory continuously, thus monitoring current levels of each item. Fixed quantity is ordered when a certain level is reached. Good: (1) Keeps constant count of inventory and (2) fixed order quantity. Bad: (1) Higher record keeping cost; (2) Periodic inventory counting is still require; (3) Time of delivery is random.

6. Session 24 Operations Management6 Continuous System with Positive Lead-time  (ROP,Q) policy Order when the inventory reaches the ROP The order size is always Q  What is the optimal Q?  How do we decide when to order? Should the re- order point be greater than dL?

7. Session 24 Operations Management7 Safety Stock  Safety Stock:  Safety Stock: Stock that is held in excess of expected demand due to variable demand rate and/or lead time. An expense of doing business. Necessary to ensure good customer service.  Safety stock is determined by demand variability and target service level.

8. Session 24 Operations Management8 Example  Daily demand for a certain product is normally distributed with a mean of 60 and a standard deviation of 7. The source of supply is reliable and maintains a constant lead time of six days. The cost of placing the order is $10 and annual holding costs are $0.50 per unit. There are no stockout costs, and unfilled orders are filled as soon as the order arrives. Assume sales occur over the entire 365 days of the year. Find the order quantity and reorder point to satisfy a 95% probability of not stocking out during the lead time. (Example 17.4, page 562)

9. Session 24 Operations Management9 Example  Let us first ignore the random/uncertainty part.  If daily demand is 60 for sure, what is the order quantity and the reorder point?

10. Session 24 Operations Management10 Example Average daily demandLeadtime z value st. dev. of demand over the leadtime

11. Session 24 Operations Management11 Example The z-value associated with 0.95 is 1.64. The re-order point R is 60(6)+1.64*17.15 = 388 units. To summarize, an order for 936 units is placed whenever the number of units remaining in inventory drops to 388.

12. Session 24 Operations Management12 Example  What happens if demand is not normal?

13. Session 24 Operations Management13 Example  What is the average on hand inventory level?

14. Session 24 Operations Management14 Example  What if the supplier is able to reduce the leadtime from 6 days to 3 days?

15. Session 24 Operations Management15 Example  What if the cost of placing an order is reduced from $10 to $2.5?

16. Session 24 Operations Management16 Inventory Level in Real Life RP Review period d1d1 Q2Q2 Target inventory level, TIL Amount used during RP+ first lead time Safety stock, SS First lead time, LT 1 LT 2 LT 3 Order 1 placed Order 2 placed Order 3 placed Shipment 1 received Shipment 2 received Shipment 3 received Time Inventory on Hand First order quantity, Q 1

17. Session 24 Operations Management17 Inventory Systems  Periodic system:  Periodic system: Physical count of items made at periodic intervals (weekly, monthly) Good: (1) Economics of scale and (2) Delivery is performed on a known schedule Bad: (1) Lack of control between reviews; (2) Carry extra stock to protect against shortages between reviews; (3) Order quantity is random

18. Session 24 Operations Management18 Periodic System  (Order-up-to,T) policy  How do we compute how much to order at every review period?  If there was no variability in the system, we would order exactly the amount needed to satisfy demand over the period T+L.

19. Session 24 Operations Management19 Example  Daily demand for a product is 10 units with a standard deviation of 3 units. The review period is 30 days, and the lead time is 14 days. Management has set a policy of satisfying 98 percent of demand from items in stock. At the beginning of this review period, there are 150 units in inventory.  How many units should be ordered? (Example 17.5, page 563)

20. Session 24 Operations Management20 Example  Let us first ignore the random/uncertainty part.  If daily demand is 10 for sure, what is the order- up-to level?  d(T+L)

21. Session 24 Operations Management21 The Safety Stock Level and Order Quantity Safety stock = z*(st. dev. of demand over review and lead time) q = d(T+L) + zσ - I Part in light blue is the target inventory level. q = Quantity to be ordered T = number of days between reviews L = lead time d = forecast avg. daily demand z = z-value for a specified service level σ = st. dev. of demand over review and lead time I = current inventory level

22. Session 24 Operations Management22 Example d = 10; T = 30; L = 14; I = 150 We must calculate z and σ. The z value for 0.98 is 2.05. Formula: q = d(T+L) + z*σ - I The quantity to order is: q = 10(30+14)+2.05*19.90-150 = 331 units to ensure 98% probability of not stocking out over the review period.

23. Session 24 Operations Management23 Example  What is the average on hand inventory level?

24. Session 24 Operations Management24 Inventory Level Safety stock, SS Time T LT-L

25. Session 24 Operations Management25 Inventory Level Safety stock, SS 3 7 6 6+20 20 6

26. Session 24 Operations Management26 Inventory Level Safety stock, SS 3 7 6 20 6 3

27. Session 24 Operations Management27 Inventory Level Safety stock, SS 3 7 6 20 3

28. Session 24 Operations Management28 Inventory Level Safety stock, SS L T-L dL dT L

29. Session 24 Operations Management29 Example  What if the supplier is able to reduce the leadtime from 14 days to 7 days?

30. Session 24 Operations Management30 Example  What if the review period is reduced from 30 days to 15 days?  What is the main trade-off that determines T, the review cycle?

31. Session 24 Operations Management31 Inventory Turn  Inventory Turn = (Annual) Cost of goods sold/Average inventory value = [(Annual) Sales quantity * Unit Cost] / (Average inventory quantity * Unit Cost) = (Annual) Sales quantity / Average inventory quantity = Throughput Rate / Average WIP = 1 / Throughput Time

32. Session 24 Operations Management32 Inventory Turn  Continuous System Inventory turn = D / (Q/2 + SS)  Periodic System Inventory turn = D / (DT/2 + SS)

33. Session 24 Operations Management33 Comparison: Continuous Review vs Periodic  Continuous review inventory system: The order quantity Q is constant (i.e., the same amount is ordered every time), and an order is placed every time the inventory drops to the reorder level R. The time between orders is variable.  Periodic review inventory system: There is a target inventory level, and an order is placed every T time units. The size of the order is variable, and equals the target inventory level minus the inventory currently on hand. The time between orders is constant.

34. Session 24 Operations Management34 The Simulation Game: First Run  Monitoring utilization rate Buy machines when the utilization rate is high  Forecasting and planning Occasional information updating and monitoring

35. Session 24 Operations Management35 The Simulation Game: First Run  Monitoring utilization rate It is very hard to play catch-up game What the cause of peak rate? Noise? Underlying demand? What is the right utilization rate for the desired leadtime?  Forecasting and planning Capacity requirement Capacity requirement with 85% target utilization rate Spreadsheet waiting time calculation for leadtime

36. Session 24 Operations Management36 The Simulation Game: First Run  Do we want to delay the purchase?  Do we want to sell the machines in the end?  Do we want to change the queue priority?

37. Session 24 Operations Management37 The Simulation Game: Second Run PreparingTesting Centrifuging Decisions: 1.Three pricing contract type (7 day, 1 day, and half day) 2.The number of machines at each station. (Start with 1.) 3.The inventory policy (reorder point, reorder quantity) 4.The priority at the testing queue (FIFO, initial, or final).

38. Session 24 Operations Management38 The Simulation Game: Second Run  Observation period for the second simulation game starts at 7:00 pm, 4/15/09 (Wed.).  Second Simulation Game Starts at 4/16/09 7:00pm (Thurs.)  The simulator stops running at 7 pm on 4/23/09 7:00pm (Thurs.)  50% is your standing against the other teams in this class.  50% is a 2 page write-up.

39. Session 24 Operations Management39 Next Class  Supply Chain Coordination Article reading: "Back to the Future: Benetton Transforms it’s Global network" MIT Sloan management Review, Fall 2001.  Beer Game Please download the game before class at http://scm.bus.umich.edu/BeerNet/Beerwin32.exe http://scm.bus.umich.edu/BeerNet/Beerwin32.exe Bring laptops to the class next time